MyWikiBiz, Author Your Legacy — Thursday November 28, 2024
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, 20:12, 3 February 2010
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| Each index <math>i</math> and exponent <math>j</math> appearing in the prime factorization of a positive integer <math>n</math> is itself a positive integer, and thus has a prime factorization of its own. | | Each index <math>i</math> and exponent <math>j</math> appearing in the prime factorization of a positive integer <math>n</math> is itself a positive integer, and thus has a prime factorization of its own. |
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| + | Continuing with the same example, the index <math>32277</math> has the factorization <math>3 \cdot 7 \cdot 29 \cdot 53 = \text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1.</math> Taking this information together with previously known factorizations allows the following replacements to be made: |
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| + | {| align="center" cellpadding="6" width="90%" |
| + | | |
| + | <math>\begin{array}{rcl} |
| + | 2 & \mapsto & \text{p}_1^1 |
| + | \\[6pt] |
| + | 3 & \mapsto & \text{p}_2^1 |
| + | \\[6pt] |
| + | 7 & \mapsto & \text{p}_4^1 |
| + | \\[6pt] |
| + | 32277 & \mapsto & \text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1 |
| + | \end{array}</math> |
| + | |} |
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| ==Riffs in Numerical Order== | | ==Riffs in Numerical Order== |